Mr Costello established the fund with an initial $60 billion to help the Commonwealth meet its superannuation obligations to retired public servants.

Labor first appointed Mr Costello to the board in 2009.

He has been acting chair of the Future Fund since January following David Gonski's switch to ANZ bank.

Mr Gonski was appointed Future Fund chairman in April 2012, but his selection was mired in a political fight.

Reports at the time suggested Mr Gonski had advised Labor that the Future Fund board wanted Mr Costello named chair.

Former treasurer Wayne Swan and former finance minister Penny Wong said Mr Gonski's advice was not a formal recommendation to government and argued Mr Gonski, and not Mr Costello, was the best man for the job.

The Coalition accused the Government of playing petty politics with the decision to overlook Mr Costello.

Labor backbencher Jim Chalmers, who served as Mr Swan's chief of staff for three years until 2010, has appeared to attack the Government's decision to appoint Mr Costello in a tweet published shortly after the decision was made public:

If only Abbott Govt put as much time, effort into jobs for av Australians as they do when it comes to putting their partisans into plum jobs